Talelli, Olympia Periodic cohomology and free and proper actions on \(\mathbb{R}^n\times S^m\). (English) Zbl 1007.20052 Campbell, C. M. (ed.) et al., Groups St. Andrews 1997 in Bath. Selected papers of the international conference, Bath, UK, July 26-August 9, 1997. Vol. 2. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 261, 701-717 (1999). This paper is structured in four sections. The first three of them give a brief survey about periodicity in Tate cohomology of finite groups, periodicity in the cohomology after some steps and generalized Tate cohomologies. In the last section it is obtained the main result: If a countable group \(G\) has periodic cohomology after 1-step then \(G\) acts freely and properly on \(\mathbb{R}^n\times S^m\), for some \(n\) and \(m\). – It is useful to mention that at the end of the paper there are given some very interesting conjectures.For the entire collection see [Zbl 0908.00018]. Reviewer: Viorel Mihai Gontineac (Iaşi) Cited in 1 ReviewCited in 2 Documents MSC: 20J06 Cohomology of groups 57M60 Group actions on manifolds and cell complexes in low dimensions 57S25 Groups acting on specific manifolds 57S30 Discontinuous groups of transformations Keywords:periodic cohomology; Tate cohomology; finite groups; free actions PDFBibTeX XMLCite \textit{O. Talelli}, Lond. Math. Soc. Lect. Note Ser. 261, 701--717 (1999; Zbl 1007.20052)